Custom float property used in a driver need manual UI modification to work
Ok I have figured out a solution.

If I save the file and reopen it, the drivers are working perfectly fine with what I have done with my script.

Might be an update issue with the property UI I don't know.

I could add a save/reopen at the end of the script, that would be an easy work around for now.

If anybody know how to instantly make it works please do tell so. Posting my answer anyway in the case someone else is encountering the same driver issue.